IRR (internal rate of return)
The IRR is the discount rate at which the present value of all cash flows of an investment, outflows and inflows, equals zero. It is the annual return implied by a project, a bond bought at a given price or an investment with irregular cash flows, and it is compared with the cost of capital to decide whether it creates value.
How it is calculated
An investment of €1,000 that returns €400 at the end of each of the next three years. We look for the rate r that satisfies 400 ÷ (1+r) + 400 ÷ (1+r)² + 400 ÷ (1+r)³ = 1,000. There is no closed-form solution: you iterate. At 10% the three flows are worth €995, too little; at 9%, €1,013, too much. The IRR is 9.70%. If the cost of capital is 8%, the project creates value; if it is 12%, it destroys value even though it returns more than it cost.
The figures in the example are invented and rounded so the arithmetic can be redone by hand. They are not data from any real company.
What it is NOT
It is not the return you will end up with: it assumes every intermediate cash flow is reinvested at the IRR itself, which is almost never possible. It does not compare projects of very different size or length (a 40% IRR on €100 is worth less than a 15% IRR on €100,000), and with cash flows that change sign several times there can be more than one IRR or none at all. That is what net present value is for.
Formula
Σ Cash flowₜ ÷ (1 + IRR)ᵗ = 0 See also
WACC (weighted average cost of capital) · Discounted cash flow (DCF) · CAGR (compound annual growth rate)
See it on real data
Celsmar computes this from the accounts companies file with their regulator, and shows which line every figure comes from. Free to start, no card.
Definition for informational purposes. It is not financial advice nor a recommendation to buy or sell.